{"id":"https://openalex.org/W2076759192","doi":"https://doi.org/10.1007/s10107-004-0569-9","title":"The Fermat rule for multifunctions on Banach spaces","display_name":"The Fermat rule for multifunctions on Banach spaces","publication_year":2005,"publication_date":"2005-02-08","ids":{"openalex":"https://openalex.org/W2076759192","doi":"https://doi.org/10.1007/s10107-004-0569-9","mag":"2076759192"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-004-0569-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-004-0569-9","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056391377","display_name":"Xi Yin Zheng","orcid":"https://orcid.org/0000-0002-5314-6471"},"institutions":[{"id":"https://openalex.org/I189210763","display_name":"Yunnan University","ror":"https://ror.org/0040axw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I189210763"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xi Yin Zheng","raw_affiliation_strings":["Department of Mathematics, Yunnan University, Kunming, 650091, P. R. China","Department of Mathematics, Yunnan University, 650091, Kunming, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yunnan University, Kunming, 650091, P. R. China","institution_ids":["https://openalex.org/I189210763"]},{"raw_affiliation_string":"Department of Mathematics, Yunnan University, 650091, Kunming, P. R. China","institution_ids":["https://openalex.org/I189210763"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014862456","display_name":"Kung Fu Ng","orcid":null},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kung Fu Ng","raw_affiliation_strings":["Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong","Department of Mathematics, The Chinese University of Hong Kong, 650091, Shatin, New Territory, Hong Kong#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong","institution_ids":["https://openalex.org/I177725633"]},{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, 650091, Shatin, New Territory, Hong Kong#TAB#","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056391377"],"corresponding_institution_ids":["https://openalex.org/I189210763"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":4.0459,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.9429028,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"104","issue":"1","first_page":"69","last_page":"90"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9095933437347412},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.7807986736297607},{"id":"https://openalex.org/keywords/fermats-last-theorem","display_name":"Fermat's Last Theorem","score":0.6768554449081421},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.5185173749923706},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4636595845222473},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.4162740111351013},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4082763195037842},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37550830841064453}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9095933437347412},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7807986736297607},{"id":"https://openalex.org/C87670640","wikidata":"https://www.wikidata.org/wiki/Q132469","display_name":"Fermat's Last Theorem","level":2,"score":0.6768554449081421},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.5185173749923706},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4636595845222473},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.4162740111351013},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4082763195037842},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37550830841064453},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10107-004-0569-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-004-0569-9","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W20559199","https://openalex.org/W55619849","https://openalex.org/W580914039","https://openalex.org/W1492700492","https://openalex.org/W1551360398","https://openalex.org/W1601960826","https://openalex.org/W1775014066","https://openalex.org/W1781163045","https://openalex.org/W1966587106","https://openalex.org/W1973407216","https://openalex.org/W1988989359","https://openalex.org/W1990596250","https://openalex.org/W1995067732","https://openalex.org/W2003660390","https://openalex.org/W2021766354","https://openalex.org/W2024057042","https://openalex.org/W2031415730","https://openalex.org/W2045034940","https://openalex.org/W2053128268","https://openalex.org/W2056543988","https://openalex.org/W2065704015","https://openalex.org/W2069876296","https://openalex.org/W2071268390","https://openalex.org/W2089533567","https://openalex.org/W2090882161","https://openalex.org/W2115871049","https://openalex.org/W2317783333","https://openalex.org/W2955198501","https://openalex.org/W2974737767","https://openalex.org/W3038830718","https://openalex.org/W4238179324"],"related_works":["https://openalex.org/W1588483307","https://openalex.org/W1966764432","https://openalex.org/W2047294383","https://openalex.org/W2004145558","https://openalex.org/W4296589634","https://openalex.org/W2031593995","https://openalex.org/W1557987663","https://openalex.org/W2165957982","https://openalex.org/W1983139066","https://openalex.org/W2963476473"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":12}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}